Integrand size = 20, antiderivative size = 20 \[ \int \frac {1}{x^2 \left (a+b \text {csch}\left (c+d \sqrt {x}\right )\right )^2} \, dx=\text {Int}\left (\frac {1}{x^2 \left (a+b \text {csch}\left (c+d \sqrt {x}\right )\right )^2},x\right ) \]
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Not integrable
Time = 0.02 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.00, number of steps used = 0, number of rules used = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int \frac {1}{x^2 \left (a+b \text {csch}\left (c+d \sqrt {x}\right )\right )^2} \, dx=\int \frac {1}{x^2 \left (a+b \text {csch}\left (c+d \sqrt {x}\right )\right )^2} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {1}{x^2 \left (a+b \text {csch}\left (c+d \sqrt {x}\right )\right )^2} \, dx \\ \end{align*}
Not integrable
Time = 69.90 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.10 \[ \int \frac {1}{x^2 \left (a+b \text {csch}\left (c+d \sqrt {x}\right )\right )^2} \, dx=\int \frac {1}{x^2 \left (a+b \text {csch}\left (c+d \sqrt {x}\right )\right )^2} \, dx \]
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Not integrable
Time = 0.23 (sec) , antiderivative size = 18, normalized size of antiderivative = 0.90
\[\int \frac {1}{x^{2} \left (a +b \,\operatorname {csch}\left (c +d \sqrt {x}\right )\right )^{2}}d x\]
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Not integrable
Time = 0.28 (sec) , antiderivative size = 44, normalized size of antiderivative = 2.20 \[ \int \frac {1}{x^2 \left (a+b \text {csch}\left (c+d \sqrt {x}\right )\right )^2} \, dx=\int { \frac {1}{{\left (b \operatorname {csch}\left (d \sqrt {x} + c\right ) + a\right )}^{2} x^{2}} \,d x } \]
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Not integrable
Time = 2.33 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.00 \[ \int \frac {1}{x^2 \left (a+b \text {csch}\left (c+d \sqrt {x}\right )\right )^2} \, dx=\int \frac {1}{x^{2} \left (a + b \operatorname {csch}{\left (c + d \sqrt {x} \right )}\right )^{2}}\, dx \]
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Not integrable
Time = 1.15 (sec) , antiderivative size = 318, normalized size of antiderivative = 15.90 \[ \int \frac {1}{x^2 \left (a+b \text {csch}\left (c+d \sqrt {x}\right )\right )^2} \, dx=\int { \frac {1}{{\left (b \operatorname {csch}\left (d \sqrt {x} + c\right ) + a\right )}^{2} x^{2}} \,d x } \]
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Not integrable
Time = 2.70 (sec) , antiderivative size = 3, normalized size of antiderivative = 0.15 \[ \int \frac {1}{x^2 \left (a+b \text {csch}\left (c+d \sqrt {x}\right )\right )^2} \, dx=\int { \frac {1}{{\left (b \operatorname {csch}\left (d \sqrt {x} + c\right ) + a\right )}^{2} x^{2}} \,d x } \]
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Not integrable
Time = 2.66 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.10 \[ \int \frac {1}{x^2 \left (a+b \text {csch}\left (c+d \sqrt {x}\right )\right )^2} \, dx=\int \frac {1}{x^2\,{\left (a+\frac {b}{\mathrm {sinh}\left (c+d\,\sqrt {x}\right )}\right )}^2} \,d x \]
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